ipsum

1 CVEN9840 – Structural Health Monitoring 2020

Dr Mehri Makki Alamdari

Assignment 2 (10% of Final Mark)

A bridge is sitting on top of four identical piers as shown in below. The bridge is subject to a ground motion as a result of an

earthquake. Assume the ground displacement is modelled as a harmonic loading ug(t)= U0sin( ഥ𝜔t) with U0 being 0.5m.

The mass of the bridge deck is Mdeck = 6×10 6 kg. The piers have a circular cross section with a height of L=10m, a radius of 3m

at the base and 1.5m at the top just under the deck.

Consider an elastic modulus of E = 20 GPa for the piers.

(1) Plot the time response of the bridge for 10 seconds under the loading if ഥ𝜔 = 𝜔𝑛

2 where 𝜔𝑛 is the natural frequency of the

bridge.

(2) Determine the maximum bending stress at the base of the pier if the excitation frequency varies between 𝜔1 = 𝜔𝑛

2 to 𝜔2 =

2𝜔𝑛 where 𝜔𝑛 is the natural frequency of the bridge.

(3) As a result of material deterioration, the elastic modulus of the material in all piers has dropped by 10%. Investigate this

damage by comparing the responses of the healthy and damaged bridge in time and frequency domain and discuss your

results. You can compare displacement, velocity, acceleration and strain time responses.

(4) If a strain gauge is installed at the outer surface of the pier in the bottom, compare the time response of strain between the

healthy and damaged bridge if the excitation frequency is 𝜔1 = 𝜔𝑛

2 .

Assumptions:

- Consider a SDOF vibration system in horizontal direction.

- Assume zero initial conditions.

- Damping ratio is 𝜁 = 10%.

- Ignore the mass of the piers.

- The stiffness is due to the piers only.

- The deck of the bridge is rigid.

- The effect of damage is only on pier stiffness.

Due at 5pm 23 October 2020. (A penalty of 10% will apply for each day of late submission for assignments.)

Online submission portal will be created on Moodle.